The probability that the selected item is less than 10.5 inches long is 0.9875
What is the probability that the selected item is less than 10.5 inches long?
To find the probability that a randomly chosen item is less than 10.5 inches long, we calculate the z-score using
z = (x - μ) / σ
where:
- x is the individual value (in this case, 10.5 inches),
- μ is the mean of the population (6.7 inches), and
- σ is the standard deviation of the population (1.7 inches).
So, we have
z = (10.5 - 6.7) / 1.7
Calculate the value of x:
z ≈ 2.24
Next, we have
P = P(z < 2.24)
Evaluate
P = 0.9875
Hence, the probability is 0.9875